The Definition of Speed pt.II

From the general and historical perspective in the definition of speed, let's have a look at the final two options:

Velocity (v) or rather speed is now defined as distance by time or d / t, and measured in km/h, m/s, mph or something equivalent.

Wikipedia: "Italian physicist Galileo Galilei is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time. In equation form, that is v=d/t"


However, I suppose Roman legions, comparing troop movements, and even ice age hunters used similar equations - it's a natural definition for a sentient being, at once a predator and prey, to cover movement in time and space, and defining it by the relation of distance to time.


Speed, defined as distance by time or d/t, increases with distance and decreases with time. This worked for eons; we instinctively appreciate speed that does so, and that speed does so.

But if you wish to validate a definition or formula, you test for the extremes - infinity and zero; zero is usually enough.

And what do we find?

for d = 0 ( immobility )

Speed = v = d/t; 0/x = 0


That's OK, but

for t = 0

Speed = v = d/t; x/0 is *not defined*


- making the formula v = d/t invalid at or near that point - and with that, universally.


For millennia, that had bothered absolutely no-one; t = 0 was an improbable condition - it meant that an object could be in two places at the same time.

And when it finally did, Einstein came along and defined the speed of light as the ultimate speed with ~300.000.000 m/s; in other words, t can never be 0, not even for the shortest of distances.

Now, whenever v = d / t nears the speed of light, relativity becomes relevant and strange things happen to time and space.

Both ends of the spectrum - zero speed ( immobility, d = 0 ) and ultimate speed ( the speed of light ) are now validly defined.

Problem solved

Now, imagine an alternative, perhaps more leisure society, where an alternative Galileo Galilei again decides to measure speed by considering the distance covered and the time it takes, but this time as Duration or "votever" (vo), the time it takes to cover a distance.

If this is hard to imagine, think of duration as a "two day's march" for a legion of soldiers or a certain stretch of ocean as a "two week's cruise" - a perfectly valid and comparable expression of - well, speed. Rapidity. Duration.

And it is in no way out of the question that this was, at least, one pre-mathematical definition of speed, again, for eons.


In equation form, that would be vo=t/d to cover movement in time and space, defined by the relation of time to space ( = time by distance ). This definition is *just as valid* as the non - alternative one.


Duration, thus defined, decreases with distance and increases with time.


Again we test for the extremes -

And what do we find?

for t = 0 (it's over already) 

Duration = vo = t/d;     0/x = 0

i. e., if the time needed to cover a certain distance is zero, then the duration to cover this distance is zero; this may be duh, and mathematically valid - but really impossible, as the alternative Einstein will invariably find out, and define the duration for light as the minimal duration of ~1/300.000.000 s/m; again, t can never be 0, not even for the shortest of distances. 

So far, so good - or rather, bad; for as it seems, t=0 would in this case be mathematically valid - but not physically.

But, before that there is again the problem of being in two places at the same time, if the distance is not 0 as well; this is because an alternative definition has no effect on reality - there is no danger of that - just on it's perception.

And, almost immediately, one can see that this variant definition is somehow much more convoluted than the primary one. Already it seems wiser not to pick it.

But even worse,

for d = 0 ( immobility )

Duration = vo = t/d;     x/0 is *not defined*


In other words, in this definition of speed, immobility is not defined.

And that is bad, as immobility exists.

Well, not really;

In the realms of infinity and eternity pertaining to the universe, there is indeed no such thing as *true* immobility; given enough space and time, everything moves against everything else.

If only the time frame is chosen big enough, no two bricks, no two rocks, no two molecules have ever not moved relative to one another; and off we go into the arguments and definitions, and those ex negativo, and qualifications, and exceptions - hey, we may even have to construe something as esoteric as "negative duration" to get out of this mess we created, by defining speed the wrong way around.

Get my drift?

Turn it around, define v as d / t, and without having misrepresented reality one way or another, all you need to throw now is one exception only, which is real, and let Einstein take care of that.

Was Galileo just lucky to pick the right one out of two possibilities, the one where the zero condition is excepted by nature (with the end speed of light), or genius enough to think it through?

We may never know. But then, again, other than entropy, speed was already known.


And so, that is what I *think* will happen if we turn Clausius' mangled definition of entropy on its head:

The mess clears up instantly

And then all we have to do is calculate *everything* once more.

Just once more.

; - )